Sensitivity Analysis for Optimization of Dynamic Systems with Reduced Order Modeling
Sensitivity Analysis for Optimization of Dynamic Systems with Reduced Order Modeling
复制标题
使用降阶建模进行动态系统优化的灵敏度分析
DOI：
10.2514/6.2010-1503
复制
发表时间：
2010
影响因子：
3.7
通讯作者：
M. Kurdi
中科院分区：
文献类型：
--
作者：
P. Beran;B. Stanford;M. Kurdi
提出了一种计算二维Navier-Stokes方程对多个潜在设计变量的灵敏度的新方法。该方法被应用到一个驱动腔的问题，其盖子以时间依赖的方式移动。结果报告验证的数值精度的计划在预测流体的响应和灵敏度的计算响应盖频率的变化。该方案的新方面涉及使用适当的正交分解，以显着减少存储敏感性分析所需数据所需的计算机内存量，这是基于时间上的伴随变量方法。灵敏度分析包括三个主要步骤：（1）计算物理响应;（2）通过本征正交分解对响应进行数据简化;以及（3）通过数据简化计算线性化解的灵敏度。并量化了与复杂系统的动态灵敏度分析相关的大量存储成本。对于低到中等复杂度的系统（线性和非线性），我们探索了动态灵敏度的计算和通过基于梯度的优化来提高系统性能。使用高阶谱时间离散获得的动力学灵敏度，研究了不同规范系统的运动学设计，研究了扑翼系统的动力学形状设计，以提高推进效率（使用直接灵敏度分析程序）和机翼的结构设计，机翼承受大的惯性驱动变形17，18。这些研究强调了通过灵敏度分析和参数变化直接操纵动态系统行为，对中等复杂性的系统进行设计优化，可以获得很大的性能优势。
A new method is developed to compute sensitivities of the Navier‐Stokes equations in two dimensions to a number of potential design variables. The method is applied to the problem of a driven cavity, whose lid moves in a time‐dependent manner. Results are reported verifying the numerical accuracy of the scheme in predicting fluidic response and the sensitivity of computed responses to changes in lid frequency. The new aspect of the scheme involves the use of the Proper Orthogonal Decomposition to reduce dramatically the amount of computer memory required to store data needed for the sensitivity analysis, which is based on the adjoint‐variable approach in time. The sensitivity analysis involves three major steps: (1) computation of physical responses; (2) data reduction of the responses via Proper Orthogonal Decomposition, and (3) computation of sensitivities about a linearized solution characterized by the data reduction. and quantified the large storage costs associated with dynamic sensitivity analysis of complex systems. For systems of low‐to‐moderate complexity (linear and nonlinear), we have explored the computation of dynamic sensitivities and the improvement of system performance through gradient‐ based optimization. examined kinematic design of different canonical systems using sensitivities of dynamics obtained with high‐order spectral temporal discretizations pursued both dynamic shape design of a flapping wing system for increased propulsive efficiency (using a direct sensitivity analysis procedure) and structural design of a wing undergoing large, inertial‐ driven deformations 17,18 . These studies highlighted the large performance advantages that could be gained through design optimization of systems of moderate complexity by direct manipulation of dynamic system behavior through sensitivity analysis and parameter variation.